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Web survey to get large \(n\) A newspaper wants to gauge public opinion about legalization of marijuana. The sample size formula indicates that it need a random sample of 875 people to get the desired margin of error. But surveys cost money, and it can only afford to randomly sample 100 people. Here's a tempting alternative: If it places a question about that issue on its website, it will get more than 1000 responses within a day at little cost. Is it better off with the random sample of 100 responses or the website volunteer sample of more than 1000 responses? (Hint: Think about the issues discussed in Section 4.2 about proper sampling of populations.)

Short Answer

Expert verified
The newspaper is better off using the random sample of 100 responses due to reduced bias and higher representativeness compared to the biased web survey.

Step by step solution

01

Understanding the Sampling Methods

There are two sampling methods being considered: a random sample of 100 people and a web survey that attracts more than 1000 responses. A random sample aims to select respondents in a way that every member of the population has an equal chance of being included, while a web survey gathers responses from those who voluntarily choose to participate.
02

Evaluating Random Sampling

Random sampling is likely to provide a representative sample of the population, as randomness reduces bias in the selection process. The small size of 100 is a drawback due to potential loss in precision of estimates (margin of error might be larger), but randomness helps ensure reliability in terms of representation.
03

Evaluating Website Volunteer Sampling

A web survey could collect thousands of responses inexpensively but generally suffers from volunteer bias. This means that responses come only from those motivated to participate, potentially skewing results toward particular opinions and not accurately representing the overall population's views.
04

Consideration of Non-Response and Biases

Non-response bias is less of a concern with the web survey due to voluntary participation; however, it does not resolve problems with selection bias. In contrast, the structured approach of a random sample addresses such biases, leading to sound statistical inferences, even with a smaller sample size.
05

Conclusion Based on Proper Sampling Techniques

Given the importance of reducing bias and obtaining a representative sample, the random sample of 100, despite being smaller, is preferable to the biased web survey. Proper sampling techniques prioritize accuracy and reliability in depicting public opinion over sheer quantity of responses.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sampling Bias
Sampling bias occurs when certain members of the population are more likely to be included in the sample than others. This results in a sample that does not accurately represent the entire population. In the context of the newspaper survey, choosing the web survey means you may end up with results skewed by sampling bias. Since it's a voluntary survey, individuals who feel strongly about the issue might be more inclined to respond, which doesn't reflect a true cross-section of the population. To reduce sampling bias, it is crucial to ensure each member of the population has an equal probability of being chosen. This can generally be achieved through random sampling, as opposed to a self-selected group, which tends to distort perceptions and findings.
Representative Sample
A representative sample is one that accurately reflects the demographics and opinions of the entire population. While conducting surveys, it is important to achieve this so that conclusions drawn can be generalized to the broader group. In this case, a properly executed random sample of 100 people, despite its smaller size, is more likely to provide a representative snapshot of public opinion on marijuana legalization compared to a non-random sample of 1000 from the web. The key lies in the sampling method – random sampling helps ensure that all population segments are included appropriately. Focusing on representation rather than quantity increases the reliability of survey results, aiding in making well-founded decisions based on data.
Survey Methodology
Survey methodology encompasses the processes used to collect data from respondents effectively. A sound survey methodology aims to reduce bias, achieve representativeness, and produce reliable results. In the newspaper's case, the methodology compares a cost-effective web survey with a random sample. While a web survey can reach many more individuals quickly and cheaply, it sacrifices the quality of insights due to lack of control over participant selection. Therefore, opting for the more expensive, yet scientifically solid random sampling method aligns better with methodological standards. The goal of survey methodology should always be to balance logistical constraints with the need to maintain accuracy and integrity in data collection.
Volunteer Bias
Volunteer bias occurs when individuals who choose to participate in a survey have different characteristics than those who do not. This typically affects the validity of results, as volunteers in surveys, like the web-based one for marijuana legalization, might hold strong opinions or possess other specific traits that differentiate them from the general population. Such bias is problematic because it can lead to incorrect generalizations. To mitigate volunteer bias, random sampling is more effective. This approach randomly picks participants, preventing self-selection from skewing the data. As a result, volunteer bias should be a primary consideration when evaluating the reliability and applicability of survey findings.

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